Being bitten is a very real risk, so I don't blame you or your husband at all for being concerned about that. And they are SO fast. In my case, Drago saw me as a rival male, so he'd chase me to attack, not mate. He saw my boyfriend as an alpha though, and wouldn't pull that behavior with him. Nonetheless, I was always the one who brought him to the vet. ;) I have a pet carrier very similar to this one - https://www.amazon.com/Soft-Crate-Kennel-Indoor-Outdoor/dp/B018IUGVLK, that I loaded Drago in from the top. I also wrapped him in a towel beforehand so he couldn't see where he was going (to the crate) or reach around to bite me as I put him in. It may sound mean, but since iguanas sleep rather soundly, you could pick him up while he's asleep/groggy and put him in a carrier during the night so he's ready to go (and not all warm/energetic) the following morning - if you can get an appointment first thing in the morning. Drago would often poop at the vet to show me how he really felt.
Mindy and Oggie